SYM-ILDL: Incomplete $LDL^{T}$ Factorization of Symmetric Indefinite and Skew-Symmetric Matrices

SYM-ILDL is a numerical software package that computes incomplete $LDL^{T}$ (or `ILDL') factorizations of symmetric indefinite and skew-symmetric matrices. The core of the algorithm is a Crout variant of incomplete LU (ILU), originally introduced and implemented for symmetric matrices by [Li and Saad, Crout versions of ILU factorization with pivoting for sparse symmetric matrices, Transactions on Numerical Analysis 20, pp. 75--85, 2005]. Our code is economical in terms of storage and it deals with skew-symmetric matrices as well, in addition to symmetric ones. The package is written in C++ and it is templated, open source, and includes a Matlab interface. The code includes built-in RCM and AMD reordering, two equilibration strategies, threshold Bunch-Kaufman pivoting and rook pivoting, among other features. We also include an efficient MINRES implementation, applied with a specialized symmetric positive definite preconditioning technique based on the ILDL factorization.